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\title{A Simple LaTeX Article}
\author{JaxEdit Project}
\date{January 12th, 2013}
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\section[Introduction]{Long Introduction}

We have the Cauchy-Schwarz inequality:
  \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
where $a_k$ and $b_k$ are real numbers, for any $k$.

\section{Calculus}

\begin{thm}
If we have the following conditions:
\begin{enumerate}
\item $f(x)$ is continuous on $[a,b]$,
\item $f(x)$ is derivable on $(a,b)$,
\item $f(a)$ and $f(b)$ have the same value,
\end{enumerate}
Then there exists $\xi\in(a,b)$ such that $f'(\xi)=0$.
\end{thm}

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